Modeling share dynamics by extracting competition structure

We propose a new method for analyzing multivariate time-series data governed by competitive dynamics such as fluctuations in the number of visitors to Web sites that form a market. To achieve this aim, we construct a probabilistic dynamical model using a replicator equation and derive its learning algorithm. This method is implemented for both categorizing the sites into groups of competitors and predicting the future shares of the sites based on the observed time-series data. We confirmed experimentally, using synthetic data, that the method successfully identifies the true model structure, and exhibits better prediction performance than conventional methods that leave competitive dynamics out of consideration. We also experimentally demonstrated, using real data of visitors to 20 Web sites offering streaming video contents, that the method suggested a reasonable competition structure that conventional methods failed to find and that it outperformed them in terms of predictive performance.